{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p11: Chebyshev differentiation of a smooth function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "from numpy import linspace,exp,sin,dot\n",
    "from matplotlib.pyplot import figure,subplot,plot,title\n",
    "from chebPy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   ],
   "source": [
    "xx = linspace(-1.0,1.0,200,True)\n",
    "uu = exp(xx)*sin(5.0*xx)\n",
    "c = 1; figure(figsize=(10,8))\n",
    "for N in [10,20]:\n",
    "    D,x = cheb(N); u = exp(x)*sin(5.0*x)\n",
    "    subplot(2,2,c); c += 1\n",
    "    plot(x,u,'o',xx,uu)\n",
    "    title('u(x), N='+str(N))\n",
    "    \n",
    "    error = dot(D,u) - exp(x)*(sin(5.0*x)+5.0*cos(5.0*x))\n",
    "    subplot(2,2,c); c += 1\n",
    "    plot(x,error,'o-')\n",
    "    title('error in u\\'(x), N='+str(N))"
   ]
  }
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